|
gptkbp:instanceOf
|
gptkb:algebraic_geometry
|
|
gptkbp:anticanonicalBundle
|
ample
|
|
gptkbp:automorphismGroup
|
varies
|
|
gptkbp:canBeSingular
|
yes
|
|
gptkbp:class
|
Iskovskih classification
finite number of families
|
|
gptkbp:containsGenus
|
varies
|
|
gptkbp:degree
|
varies
|
|
gptkbp:dimensionOfAnticanonicalLinearSystem
|
varies
|
|
gptkbp:dimensions
|
3
|
|
gptkbp:example
|
projective 3-space
cubic threefold
intersection of two quadrics in P^5
quartic double solid
|
|
gptkbp:fieldOfStudy
|
gptkb:algebraic_geometry
|
|
gptkbp:genus
|
integer invariant
|
|
gptkbp:hasCanonicalBundle
|
negative
|
|
gptkbp:hasDiscriminant
|
varies
|
|
gptkbp:hasHodgeNumbers
|
varies
|
|
gptkbp:hasInvariant
|
gptkb:genus
gptkb:university
gptkb:nun
gptkb:Picard_number
discriminant
|
|
gptkbp:hasModuliSpace
|
yes
|
|
gptkbp:hasPicardNumber
|
varies
|
|
gptkbp:hasProperty
|
gptkb:Fano_variety
|
|
gptkbp:hasRationalityProblem
|
yes
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
Fano threefold
|
|
gptkbp:importantFor
|
birational geometry
moduli theory
classification theory
|
|
gptkbp:indexedIn
|
1, 2, 3, or 4
|
|
gptkbp:isDefinedOver
|
algebraically closed field
|
|
gptkbp:isProjective
|
yes
|
|
gptkbp:isRational
|
not always
|
|
gptkbp:isSmooth
|
can be smooth
|
|
gptkbp:isUnirational
|
sometimes
|
|
gptkbp:namedAfter
|
gptkb:Gino_Fano
|
|
gptkbp:PicardNumber
|
at most 10
|
|
gptkbp:relatedTo
|
gptkb:Fano_variety
gptkb:Mori_theory
gptkb:del_Pezzo_surface
gptkb:minimal_model_program
Fano surface
|
|
gptkbp:studiedIn
|
birational geometry
algebraic geometers
|
|
gptkbp:usedIn
|
classification of algebraic varieties
|
|
gptkbp:bfsParent
|
gptkb:Fano_threefolds_classified_by_Iskovskih_and_Mori–Mukai
|
|
gptkbp:bfsLayer
|
7
|